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Merge branch 'master' of https://github.com/iqiukp/KPCA-MATLAB
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README.md

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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/helix.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/helix.png">
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</p>
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<h3 align="center">Kernel Principal Component Analysis (KPCA)</h3>
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<p align="center">MATLAB Code for dimensionality reduction, fault detection, and fault diagnosis using KPCA</p>
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<p align="center">MATLAB code for dimensionality reduction, fault detection, and fault diagnosis using KPCA</p>
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<p align="center">Version 2.2, 14-MAY-2021</p>
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<p align="center">Email: [email protected]</p>
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/helix.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/helix.png">
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</p>
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Another application using banana-shaped data:
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/banana.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/banana.png">
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</p>
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/circle.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/circle.png">
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</p>
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kplot.cumContribution(kpca)
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/cumContirb.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/cumContirb.png">
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</p>
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As shown in the image, when the number of components is 21, the cumulative contribution rate is 75.2656%,which exceeds the given explained level (0.75).
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kplot.cumContribution(kpca)
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```
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<p align="center">
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<img width="60%" height="60%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/components.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/components.png">
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</p>
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As shown in the image, when the number of components is 24, the cumulative contribution rate is 80.2539%.
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/FD_train.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/FD_train.png">
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</p>
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The test results are
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/FD_test.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/FD_test.png">
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</p>
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### 06. Fault diagnosis
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```
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<p align="center">
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<img width="70%" height="70%" src="https://github.com/iqiukp/Kernel-Principal-Component-Analysis-KPCA/blob/master/imgs/diagnosis.png">
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<img src="http://github-files-qiu.oss-cn-beijing.aliyuncs.com/KPCA-MATLAB/diagnosis.png">
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</p>
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